Melt the butter in a large (12-inch) skillet over medium heat. Add the shallots and garlic. Sauté until the shallots are softened but not quite beginning to brown, about 10 minutes.

Add the mushrooms to the skillet and sprinkle them with salt. Sauté until all of the liquid has evaporated and mushrooms have just started to brown, about 10 minutes. Add the thyme leaves and sauté for 1 more minute.

Pour in the wine and stir. Let simmer until the liquid is fully evaporated and you can hear a little bit of sizzle in the pan, about 5 minutes. Turn off the heat and let stand for 5 minutes.

Toast the slices of baguette until golden. Spread each toast with goat cheese and top with the mushrooms.